I was able to use almost everyone's suggestions to pull this off! I ended up with just wild birds - one was a bit shot up, so I only used the breast from it. They were also skinned, so that made it impossible to do the butter under the skin thing.
Anyway - I read on a game cooking website that pheasant benefits from brining, so I did that for a few hours.
Then I made a "rack" out of celery, and put a few cups of pear cider in the bottom, and sprinkled it with sauerkraut.
The birds got stuffed with a mix of apples, onions, lemons & sauerkraut.
Then they were coated with herbed butter, then topped with thick slices of pancetta.
They went into a very cranky egg that refused to maintain any one temp for about 4 hours. I tried to keep the temp at about 275 - 300, but I cranked it up at the end because I thought they weren't done & I panicked a bit.
They turned out ok - a bit dry, but I am told that's the way they are. hmmmph.
Thanks for all the suggestions & help, and of course, thank you Max for the call walking me through the whole mess!!